Nuclei

Nuclei

Team Careers360Updated on 19 Sep 2025, 12:46 PM IST

Nucleus is the dense heavy core found at the center of an atom. It holds the protons (positive charge) and neutrons (Chargeless) together. The entire mass of an atom is in the nucleus while electrons simply surround it in a cloud. Protons and neutrons are bound together by a unique strong force known as the nuclear force. The force is extremely strong but only acts at very short distances. While the nucleus is small it has an enormous impact in science ranging from the study of radioactivity and nuclear energy to how stars generate energy.

Nuclei
Nuclei

Nuclei Class 12th Topics (NCERT Syllabus)

1. Introduction

This chapter deals with the structure of the nucleus, its size, mass, stability, and important nuclear phenomena like radioactivity, nuclear fission, and fusion that play a major role in science and technology.

2. Atomic Masses and Composition of Nucleus

The nucleus is made up of protons and neutrons, together called nucleons.

  • Atomic number (Z): Number of protons.
  • Mass number (A): Total number of protons and neutrons.
  • Number of neutrons (N): $N=A-Z$.

The mass of an atom is concentrated in the nucleus since electron mass is negligible.
The unit of atomic mass is $\mathbf{1}$ atomic mass unit ( $\mathbf{1 u}$ ):

$
1 u=\frac{1}{12} \text { mass of a carbon- } 12 \text { atom }=1.66 \times 10^{-27} \mathrm{~kg} \text {. }
$


The nucleus of an element is represented as:

$
{ }_Z^A X
$

where $\mathbf{X}$ is the chemical symbol, $\mathbf{Z}$ is the atomic number, and $\mathbf{A}$ is the mass number.

3. Size of the Nucleus

The nucleus is extremely small compared to the size of an atom.
Nuclear radius is given by the empirical formula:

$
R=R_0 A^{1 / 3}
$

where

$
R_0 \approx 1.2 \times 10^{-15} \mathrm{~m},
$

and $A$ is the mass number.

  • Thus, the nuclear radius increases with $A^{1 / 3}$, while the volume is proportional to A .
  • This means nuclear matter has approximately constant density, independent of the size of the nucleus.
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4. Mass–Energy and Nuclear Binding Energy

Einstein's relation $E=m c^2$ shows mass and energy equivalence. The mass of a nucleus is less than the sum of masses of its protons and neutrons. This difference, called mass defect, corresponds to the binding energy of the nucleus. Binding energy is the energy needed to separate a nucleus into its nucleons. The binding energy per nucleon determines the stability of the nucleus-greater value means higher stability.

5. Nuclear Force

The stability of a nucleus shows the existence of a new fundamental force, called the nuclear force. It is the attractive force that binds protons and neutrons (nucleons) together in the nucleus. Nuclear force is:

  1. Very strong compared to gravitational and electrostatic forces.
  2. Short-ranged (effective up to a few femtometres).
  3. Charge-independent (acts equally between proton–proton, neutron–neutron, and proton–neutron).
  4. Saturating in nature (each nucleon interacts only with its nearest neighbours).

6. Radioactivity

Radioactivity is the spontaneous emission of particles (α, β) or electromagnetic radiation (γ-rays) from the nucleus of certain unstable atoms. It was discovered by Henri Becquerel (1896) and further studied by Marie and Pierre Curie.

Three types of radioactive decay occur in nature :
(i) $\alpha$-decay in which a helium nucleus ${ }_2^4 \mathrm{He}$ is emitted;
(ii) $\beta$-decay in which electrons or positrons (particles with the same mass as electrons, but with a charge exactly opposite to that of electron) are emitted;
(iii) $\gamma$-decay in which high energy (hundreds of keV or more) photons are emitted.

7. Nuclear Energy

Nuclear energy is the energy released from the nucleus of an atom during nuclear reactions such as fission (splitting of a heavy nucleus) and fusion (joining of light nuclei). This energy comes from the conversion of a small amount of mass into energy, as given by Einstein's relation:

$
E=m c^2
$

Nuclear fission (used in nuclear reactors and atomic bombs) releases large energy when heavy nuclei like uranium-235 or plutonium-239 split into lighter nuclei.
Nuclear fusion (occurs in the sun and hydrogen bombs) releases even more energy when light nuclei like hydrogen isotopes combine to form helium.
Nuclear energy is a powerful source of electricity and medical applications but requires careful handling due to radioactive waste and safety concerns.

Related Topics,

Nuclei Class 12 Important Formula

These are the most used formulas for boards and competitive exams (JEE/NEET):

  • Atomic mass unit: $1 u=931 \mathrm{MeV} / c^2$
  • Mass-energy relation: $E=m c^2$
  • Binding energy (B.E.):
    $\text { B.E. }=\left[Z m_p+(A-Z) m_n-M\right] c^2$

  • Binding energy per nucleon:
    $\frac{B . E .}{A}$

  • Radioactive decay law:
    $N=N_0 e^{-\lambda t}$
  • Half-life:
    $T_{1 / 2}=\frac{0.693}{\lambda}$
  • Mean life:$\tau=\frac{1}{\lambda}$
  • Activity:$R=\lambda N$

Exam-wise Weightage of Nuclei

ExamApproximate WeightageRemarks
NEETUp to 1 QuestionMostly theory-based questions on radioactivity, half-life, and binding energy.
Board4 MarksFocus on derivations (mass-energy relation, binding energy) and numericals.
JEEUp to 1 QuestionConceptual + numerical problems on nuclear reactions, radioactivity, and energy release.

NCERT Notes Subject wise link:

NCERT Solutions Subject wise link:

NCERT Exemplar Solutions Subject wise link:

Frequently Asked Questions (FAQs)

Q: What is the definition of a nucleus?
A:

It is characterised as a collection of positively charged protons and electrically neutral neutrons. Quarks are the particles that makeup neutrons and protons.

Q: What are the topics taught in Nuclear Physics?
A:

Nuclear weapons, nuclear power, medicine, magnetic imaging resonance, ions implantation, engineering, cultural and industrial isotopes, radiocarbon dating in geology, and nuclear engineering are some of the themes covered.

Q: Why are there always more protons than neutrons in stable nuclei?
A:

Protons are positively charged sections of the atom, which means they oppose each other electrically. When there are more than 10 protons in a nucleus, this repulsion becomes excessive. As a result, a higher number of neutrons, which create only attractive forces, is required for stability.

Q: Is it possible to conclude that electrons exist inside the nucleus based on beta decay?
A:

No, despite being an electron, the beta particle is generated and expelled at the same time as beta decay. It will be unable to exist within the nucleus due to the de-Broglie wavelength, which is far bigger than the nucleus' size.

Q: The total mass of a nucleus' components – neutrons and protons – is always smaller than the mass of the nucleus in its ground state. Explain.
A:

When nucleons come together to form a nucleus, they are strongly attracted to one another. Their potential energy is dwindling and turning negative. The nucleons in the nucleus are held together by this potential energy. As the potential energy of the nucleon decreases, the mass of the nucleon inside the nucleus decreases as well.